I have built an audio sharing application (pretty similar to soundcloud.com, but focused on a niche and just one country). I'd like to enable people to hear the tracks directly from Facebook, like they can do it with eg. Spotify.
I am having a trouble with getting development docs on how to do that.

If you just want users to be able to embed a player in posts/likes of your content, any app can do this with the use of meta tags on the pages, and this is covered under 'Attaching Audio and Video Data' on the Open Graph documentation